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A176999
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An encoding of the Collatz iteration of n.
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3
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1, 1111010, 11, 11110, 11110101, 1111011101101010, 111, 1111011101101010110, 111101, 11110111011010, 111101011, 111101110, 11110111011010101, 11110111110101010, 1111, 111101110110, 11110111011010101101, 11110111011010111010, 1111011, 1111110, 111101110110101
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OFFSET
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2,2
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COMMENTS
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Working from right to left, the sequence of 0's and 1's in a(n) encode, respectively, the sequence of 3x+1 and x/2 steps in the Collatz iteration of n. This is reverse one's complement of Garner's parity vector. Criswell mentions this encoding.
The length of a(n) is A006577(n). The number of 1's in a(n) is A006666(n). The number of 0's in a(n) is A006667(n). The number of terms having length k is A005186(k).
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LINKS
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EXAMPLE
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a(5)=11110 because the Collatz iteration for 5 is a 3x+1 step (0) followed by 4 x/2 steps (four 1's).
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MATHEMATICA
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encode[n_]:=Module[{m=n, p, lst={}}, While[m>1, p=Mod[m, 2]; AppendTo[lst, 1-p]; If[p==0, m=m/2, m=3m+1]]; FromDigits[Reverse[lst]]]; Table[encode[n], {n, 2, 26}]
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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